Answer:
C
Step-by-step explanation:
In order to solve these you have to use pemdas, which is the order for which you solve these equations from left to right.
Its, parenthesis, exponents, multiplication, division, addition, subtraction.
when using this strategy it will show that
a=48
b=76
c=91
d=63
The function g(x) = x2 is transformed to obtain function h:
h(x) = g(x) – 5.
Which statement describes how the graph of his different from the graph of g?
A.
The graph of h is the graph of g horizontally shifted right 5 units.
B.
The graph of h is the graph of g vertically shifted up 5 units.
C.
The graph of h is the graph of g vertically shifted down 5 units.
OD.
The graph of h is the graph of ghorizontally shifted left 5 units.
Answer:
Option C
The graph of g is vertically shifted 5 units down
Gerald graphs the function f(x) = (x – 3)2 – 1. Which statements are true about the graph? Select three options.
Answer:
The answer is "Choice B, C, and F is correct".
Step-by-step explanation:
The following are choices, which is missing in the question, that can be defined as follows:
A) {x| x ≥ 3} is the domain.
B) The set shall be {y| y ≥ –1}.
C) over the interval (–∞, 3), is the function, that decreases.
D) it's over the duration the function increases its value, that is (–1, ∞).
E) The symmetry axis will be x = – 1.
F) vertex is (3, – 1).
In choice A, It is incorrect even though f is the domain, which is all true numbers because it has a quadrant function. In choice B, it is correct. In choice C, It is valid because it was a parable open with vertex so if we exploded view f (3, -1). Because as value opens up, its value with x from-∞ to 3 drops while it goes up from increasing from 3 to ∞. In choice D, It is wrong since we have just said f decreases from-∞ to 3. Therefore, f decreases from -1 to 3, too. Therefore, f doesn't grow from -1 to ∞. In choice E, It is incorrect because the symmetry axis is x = 3. In choice F, it is true.Answer:
the answers are b, c, e
Step-by-step explanation:
i just took the test
True or False. The statistician should use Printout C to perform a t-test on the GROUP variable in the regression model. g
Answer:
False
Step-by-step explanation:
Regression model is a set of statistical process which estimates the relationship between two variables. The one variable is dependent variable and the other is independent variable. The statistician should not use printout C to perform a t-test in regression model.
Please help. I’ll mark you as brainliest if correct
Answer:
(a)
dependent
(b)
x = -3t - 12
y = -5t - 16
z = t
Step-by-step explanation:
2x - 3y - 9z = 24 Eq. 1
x + 3z = -12 Eq. 2
-3x + y - 4z = 20 Eq. 3
2x - 3y - 9z = 24
(+) -9x + 3y - 12x = 60 3 * Eq. 3
--------------------------------
-7x -21z = 84 Eq. 4
7x + 21z = -84 7 * Eq. 2
(+) -7x - 21z = 84 Eq. 4
-----------------------------
0 = 0
(a) The system is dependent.
(b)
z = t
x + 3z = -12 Eq. 2
x + 3t = -12
x = -3t - 12
2x - 3y - 9z = 24 Eq. 1
2(-3t - 12) - 3y - 9t = 24
-6t - 24 - 3y - 9t = 24
-3y - 15t = 48
-y - 5t = 16
-y = 5t + 16
y = -5t - 16
x = -3t - 12
y = -5t - 16
z = t
what is the radius for a circle whose equation is x2 + y2 = 64
Answer:
radius of 8Step-by-step explanation:
step one :
Given that the equation of the circle is described as
[tex]x^2 + y^2 = 64[/tex]
To correctly identify the center of the circle we have to place the equation in the standard form.
the standard equation for a circle is
[tex](x-h)^2+(x-k)^2= r^2[/tex]
step two :
let us re-write the given equation so that we can compare it with the general equation of circle
[tex](x-0)^2+(x-0)^2= 8^2[/tex]
step three:
From this above equation in step two we can see that the circle has a radius of 8
Eliminate the parameter for the following set of parametric equations: x= t^2 + 2 y= 4t^2
Answer:
Solution : y = 4x - 8
Step-by-step explanation:
The first thing we want to do is isolate t², rather than t. Why? As you can see when we substitute t² into the second equation, it will be easier than substituting t, as t is present in the form t². So, let's isolate t² in the first equation --- ( 1 )
x = t² + 2,
t² = x - 2
Now let's substitute this value of t² in the second equation --- ( 2 )
y = 4t²,
y = 4(x - 2),
y = 4x - 8 ~ And hence our solution is option c.
It has been found that 26% of men 20 years and older suffer from hypertension (high blood pressure) and 31.5% of women are hypertensive. A random sample 150 of each gender was selected from recent hospital records, and the following results were obtained. Construct 95% confidence interval for the difference of the two proportion. Round your answer to nearest ten-thousandth. Interpret the result.
Complete Question
It has been found that 26% of men 20 years and older suffer from hypertension (high blood pressure) and 31.5% of women are hypertensive. A random sample 150 of each gender was selected from recent hospital records, and the following results were obtained.
Men. 43 patients had high blood pressure
Woman. 52 patients had high blood pressure.
Answer:
The 95% confidence interval is
[tex]- 0.1651 < p_m - p_f <0.0451[/tex]
This mean that there is a 95 % confidence that the difference between the true proportions of male and female that are hypertensive is within this interval and given that the interval contains zero then there is no statistically significant difference between the genders that are hypertensive
Step-by-step explanation:
From the question we are told that
The sample size for male is [tex]n_1 = 150[/tex]
The number of male that are hypertensive is [tex]m = 42[/tex]
The sample size of female is [tex]n_2 = 150[/tex]
The number of female that are hypertensive is [tex]q = 52[/tex]
The proportion of male that are hypertensive is mathematically represented as
[tex]\r p_m = \frac{43}{150}[/tex]
[tex]\r p_m = 0.287[/tex]
The proportion of female that are hypertensive is mathematically represented as
[tex]p_f = \frac{52}{150}[/tex]
[tex]p_f = 0.347[/tex]
From the question we are told that confidence level is 95%, hence the level of significance is mathematically represented as
[tex]\alpha = 100 -95[/tex]
[tex]\alpha =5\%[/tex]
[tex]\alpha =0.05[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{ \r p_m (1- \r p_m )}{n_1} + \frac{ \r p_f (1- \r p_f )}{n_2} }[/tex]
substituting value
[tex]E = 1.96 * \sqrt{\frac{ 0.287 (1- 0.287 )}{150} + \frac{ 0.347 (1- 0.347 )}{150} }[/tex]
[tex]E = 0.1051[/tex]
The 95% confidence interval is mathematically represented as
[tex](\r p_m - \r p_f ) - E < p_m - p_f < (\r p_m - \r p_f ) + E[/tex]
substituting values
[tex]( 0.287 - 0.347 ) - 0.1051 < p_m - p_f <( 0.287 - 0.347 ) + 0.1051[/tex]
[tex]- 0.1651 < p_m - p_f <0.0451[/tex]
This mean that there is a 95 % confidence that the difference between the true proportion is within this interval and given that the interval contains zero then there is no statistically significant difference between the genders that are hypertensive.
Does coordinate x or coordinate y represent a greater number?
Answer:
Y
Step-by-step explanation:
You see that (x,3) and (2,7) are on the exact same x-value, which is 2. Y, on the other hand, is on the same y-value as (4,3), so it's going to be 4. 4 > 2, so your answer is y.
Y represents the greater number.
We see that (x,3) and (2,7) are on the exact same x-value, which is 2. Y, on the other hand, is on the same y-value as (4,3), so it's going to be 4. 4 > 2, so your answer is y.
What is an example of a coordinate?A set of values that display an actual role. On graphs it is also a pair of numbers: the first variety indicates the gap along, and the second variety indicates the distance up or down. As an example, the factor (12,5) is 12 units long, and five units up.
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Jamar rolls a 6-sided number cube with the numbers 1 through 6 on it. What is the
probability that he does not roll a prime number?
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
In a 6 sided die, the numbers that are possible to be rolled are
1, 2, 3, 4, 5, and 6.
We know that the numbers 2, 3, and 5 are prime, while 1, 4, and 6 are not.
3 out of the 6 numbers are prime, therefore 3 out of the 6 numbers are not prime.
So the fraction is [tex]\frac{3}{6}[/tex]
This simplifies to [tex]\frac{1}{2}[/tex].
Hope this helped!
Answer:
1/2
Step-by-step explanation:
the prime numbers between 1 and 6 inclusive are: 2, 3, 5 (i.e 3 possible outcomes)
the non prime numbers are : 1, 4 and 6 (i.e 3 possible outcomes)
for each roll, the total number of possible outcomes is 6 (because its a 6-sided die)
P(does not roll a prime number) = P (rolls 1, 4 or 6)
= number of possible non-prime outcomes / total number of outcomes
= 3/6
= 1/2
Pentagon ABCDE and pentagon A”B”C”D”E” are shown on the coordinate plane below. Which two transformations are applied to pentagon ABCDE to create A”B”C”D”E”?
Answer:
Translated according to the rule (x, y)⇒ (x+7, y+1) , reflected across the x-axis
Step-by-step explanation:
Transformation involves changing the orientation, or even size of a given figure or object to produce its image. The methods of transformation include; translation, rotation, reflection, and dilation.
Comparing the pentagon ABCDE and A”B”C”D”E”, the two transformations applied are reflection across the x-axis first, then translation.
The diameter of a large lawn ornament in the shape of a sphere is 16 inches. What is the approximate volume of the ornament? Use 3.14 for Pi. Round to the nearest tenth of a cubic inch. Recall the formula V = four-thirds pi r cubed.
Answer:
Sphere Volume = 4/3 * PI * radius^3
Sphere Volume = 4/3 * PI * 8^3
Sphere Volume = 4/3 * PI * 512
Sphere Volume = 2,144.7 cubic inches
Step-by-step explanation:
Two hot air balloons are flying above a park. One balloon started at a height of 3,000 feet above the ground and is decreasing in height at a rate
of 40 feet per minute. The second balloon is rising at a rate of 50 feet per minute after beginning from a height of 1.200 feet above the ground.
Given that his the height of the balloons after m minutes, determine which system of equations represents this situation.
Answer:
a
Step-by-step explanation:
its a
The answer is m = 3000 - 40h
m = 1200 + 50h.
The answer is option A.
What is a problem in problem-solving?
Problem-solving is the act of defining a problem; figuring out the reason for the hassle; identifying, prioritizing, and selecting options for an answer; and enforcing an answer.
What is an example of problem-solving?Problem-solving begins with identifying the issue. For example, a teacher would possibly need to parent out a way to enhance scholar performance on writing scalability take a look at it. To do this, the trainer will assess the writing tests seeking out regions for improvement.
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Which of the following classifications of polygons could be a valid description? an equilateral scalene triangle an obtuse scalene triangle a square trapezoid a rectangular kite
Answer:
B. An obtuse scalene triangle
Step-by-step explanation:
Polygons are plane figures bounded by three or more straight sides. Examples are: trigon, quadragon, hexagon, nonagon etc. They are named with respect to their number of sides.
An obtuse triangle has one of its angles greater than [tex]90^{0}[/tex] but less than [tex]180^{0}[/tex]. While a scalene triangles has non of its sides to be equal in length.
The valid description of the classes of polygons is: an obtuse scalene triangle. Which implies that the triangle has one of its angles to be obtuse, and non of its sides equal.
Given two points M & N on the coordinate plane, find the slope of MN , and state the slope of the line perpendicular to MN . (there's two questions)
1) M(9,6), N(1,4)
2) M(-2,2), N(4,-4)
Answer:
Problem 1) [tex] m = \dfrac{1}{4} [/tex] [tex] slope_{perpendicular} = -4 [/tex]
Problem 2) [tex] m = \dfrac{1}{3} [/tex] [tex] slope_{perpendicular} = -3 [/tex]
Step-by-step explanation:
[tex] slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex] slope_{perpendicular} = \dfrac{-1}{m} [/tex]
Problem 1) M(9,6), N(1,4)
[tex] slope = m = \dfrac{6 - 4}{9 - 1} = \dfrac{2}{8} = \dfrac{1}{4} [/tex]
[tex] slope_{perpendicular} = \dfrac{-1}{\frac{1}{4}} = -4 [/tex]
Problem 2) M(-2,2), N(4,-4)
[tex] slope = m = \dfrac{4 - 2}{4 - (-2)} = \dfrac{2}{6} = \dfrac{1}{3} [/tex]
[tex] slope_{perpendicular} = \dfrac{-1}{\frac{1}{3}} = -3 [/tex]
renea is going to the lake to visit some freinds if the lake is 60 miles away and renae is driving at 40 miles per hour the entire time how long will it take her to get to the lake
Answer:
1.5 hours
Step-by-step explanation:
Set up a proportion:
[tex]\frac{40 miles}{1 hour}[/tex] = [tex]\frac{60 miles}{x}[/tex]
Cross multiply:
40x = 60
x = 1.5
= 1.5 hours
A bike wheel. A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?
Answer:
The answer is 660.4 millimetersStep-by-step explanation:
Diameter = 26 inches
From the question
1 inch = 25.4 mm
To find it's equivalent in millimeters multiply 26 inches by 25.4 millimeters and divide by 1 inch
so we have 26 inches as
[tex] \frac{26 \: inches \times 25.4mm}{1 \: inch} [/tex]
Simplify
We have
26 × 25.4 mm
We have the final answer as
660.4 millimetersHope this helps you
Answer: B.) 26 inches (25.4 millimeters/ 1 inch)
Step-by-step explanation: i hope this helps :)
According the the U.S. Department of Education, full-time graduate students receive an average salary of $15,000 with a standard deviation of $1,200. The dean of graduate studies at a large state university in PA claims that his graduate students earn more than this. He surveys 100 randomly selected students and finds their average salary is $16,000. Use a significance level of 0.05 to test if there is evidence that the dean's claim is correct. What are the hypotheses
Answer:
Step-by-step explanation:
Given that :
population Mean = 15000
standard deviation= 1200
sample size n = 100
sample mean = 16000
The null and the alternative hypothesis can be computed as follows:
[tex]\mathtt{H_o : \mu = 15000 }\\ \\ \mathtt{H_1 : \mu > 15000}[/tex]
Using the standard normal z statistics
[tex]z = \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}[/tex]
[tex]z = \dfrac{16000 -15000}{\dfrac{1200 }{\sqrt{100}}}[/tex]
[tex]z = \dfrac{1000}{\dfrac{1200 }{10}}[/tex]
[tex]z = \dfrac{1000\times 10}{1200}[/tex]
z = 8.333
degree of freedom = n - 1 = 100 - 1 = 99
level of significance ∝ = 0.05
P - value from the z score = 0.00003
Decision Rule: since the p value is lesser than the level of significance, we reject the null hypothesis
Conclusion: There is sufficient evidence that the Dean claim for his graduate students earn more than average salary of $15,000
Dean's Claim of Average Salary = 16000, ie greater than 15000 : is correct
Null Hypothesis [ H0 ] : Average Salary = 15000
Alternate Hypothesis [ H1 ] : Average Salary > 15000
Hypothesis is tested using t statistic.
t = ( x - u ) / ( s / √ n ) ; where -
x = sample mean , u = population mean , s = standard deviation, n = sample size
t = ( 16000 - 15000 ) / ( 1200 / √100 )
= 1000 / 120
t {Calculated} = 8.33,
Degrees of Freedom = n - 1 = 100 = 1 = 99
Tabulated t 0.05 (one tail) , at degrees of freedom 99 = 1.664
As Calculated t value 8.33 > Tabulated t value 1.664 , So we reject the Null Hypothesis in favour of Alternate Hypothesis.
So, conclusion : Average Salary > 15000
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Determine the present value P that must be invested to have the future value A at simple interest rate r after time t.
A = $8000.00, r = 10.5%, t = 9 months
$
(Round up to the nearest cent as needed.)
Answer:
$7,415.99
Step-by-step explanation:
Hello, please consider the following.
[tex]P\cdot (1+\dfrac{10.5\%\cdot 9}{12})=A = 8000 \\\\P = \dfrac{8000}{(1+\dfrac{31.5}{400})}=\dfrac{8000}{1.07875}\\\\=7415.990730...[/tex]
So it gives $7,415.99
Thank you.
WILLL GIVE ALL MY POINT PLUS MARK BRAILIEST PLS HELP ASAP TY <3
Answer:
The unknown integer that solves the equation is 6.
Step-by-step explanation:
In order to find the missing number, we can set up an equation as if we are solving for x.
x + (-8) = -2
Add 8 on both sides of the equation.
x = 6
So, the unknown integer is 6.
Answer:
6
Step-by-step explanation:
6 plus -8 is -2
For the given data value, find the standard score and the percentile. A data value 0.6 standard deviations above the mean.
Answer:
The z-score is [tex]z = 0.6[/tex]
The percentile is [tex]p(Z < 0.6) = 72.57\%[/tex]
Step-by-step explanation:
From the question we are told that
The data value is 0.6 standard deviations above the mean i.e [tex]x = \mu + 0.6 \sigma[/tex]
Where [tex]\mu[/tex] is the population mean and [tex]\sigma[/tex] is the standard deviation
Generally the z-score is mathematically represented as
[tex]z = \frac{x - \mu }{\sigma }[/tex]
=> [tex]z = \frac{(\mu + 0.6\sigma ) - \mu }{\sigma }[/tex]
=> [tex]z = 0.6[/tex]
The percentile is obtained from the z-table and the value is
[tex]p(Z < 0.6) = 0.7257[/tex]
=> [tex]p(Z < 0.6) = 72.57\%[/tex]
Find a • b. a = 5i + 7j, b = -4i + 3j
Answer:
[tex]a \cdot b = 1[/tex]
Step-by-step explanation:
[tex] a = 5i + 7j [/tex]
[tex] b = -4i + 3j [/tex]
[tex] a = a_xi + a_yj [/tex]
[tex]b = b_xi + b_yj[/tex]
[tex] a \cdot b = a_xb_x + a_yb_y [/tex]
[tex] a \cdot b = (5)(-4) + (7)(3) [/tex]
[tex] a \cdot b = -20 + 21 [/tex]
[tex]a \cdot b = 1[/tex]
Answer:
[tex]\boxed{-20i^2 -13ij+21j^2}[/tex]
Step-by-step explanation:
[tex]\sf Plug \ in \ the \ values.[/tex]
[tex](5i+7j) \cdot (-4i+3j)[/tex]
[tex]\sf Expand \ brackets.[/tex]
[tex]5i(-4i+3j)+7j(-4i+3j)[/tex]
[tex]-20i^2 +15ij+-28ij +21j^2[/tex]
[tex]\sf Combine \ like \ terms.[/tex]
[tex]-20i^2 -13ij+21j^2[/tex]
-58.58 is equal to the rational number
Answer:
This is true
Step-by-step explanation:
Because a rational number can be expressed as going on forever.
What is the solution to X+9 = 24?
A. x = 33
B. x= 15
C. x= 18
D. x= 9
Answer:
X+9=24
Or,x=24-9
:.x=15
Step-by-step explanation:
Answer:
B. x=15
Step-by-step explanation:
To find the solution to the equation, we must get x by itself on one side of the equation.
[tex]x+9=24[/tex]
9 is being added to x. The inverse of addition is subtraction. Subtract 9 from both sides of the equation.
[tex]x+9-9=24-9[/tex]
[tex]x=24-9[/tex]
[tex]x=15[/tex]
Let's check our solution. Plug 15 in for x.
[tex]x+9=24 (x=15)[/tex]
[tex]15+9=24[/tex]
[tex]24=24[/tex]
This checks out, so we know our solution is correct. The answer is B. x=15
Find the value of the variable x in the equation x - 21 = 8.
A) -13
B) 29
C) -29
D) 13
Answer: x=29
Step-by-step explanation:
[tex]x-21=8[/tex]
add 21 to both sides
[tex]x-21+21=8+21[/tex]
[tex]21+8=29\\[/tex]
[tex]x=29[/tex]
Sammy the Sailor swears entirely too much. The following probability distribution shows the number of times Sammy swears per day and the corresponding probabilities:
# of swear words: 2 5 9 14 20
Probability: 0.01 0.09 0.30 0.40 0.20
In an effort to reduce his amount of swearing, Sammy places $1.00 in a jar every time he swears. Further, if at the end of the day he swears more than 10 times, he places an extra $2.00 in the jar per swear word over 10. If Sammy swears less than 5 times, he takes out $0.50 for each of his swear words.
A B C D E F G
1 # of swear word Probability
2 Cost per swear word $1.00 2 0.01
3 Extra cost per swear
word over 10 $2.00 5 0.09
4 Refund per swear word
less than 5 $0.50 9 0.3
5 14 0.4
6 20 0.2
7
8
9 # Regular Extra cost Refund Total
swear swear if over 10 if under money
words word swear 5 swear in the jar
cost words words for the
day
10
Based off the partial simulation spreadsheet above, answer the following questions:
A) What formula should go into cell C10 to calculate the Regular Swear word cost?
B3*B4 SUMPRODUCT(B2:B4, B10) B4*B10 SUM(B2:B4) B2*B10 B3*B2 B3*B10
B) What formula should go into cell D10 to calculate the Extra Swear word cost?
=IF(B10>10,(B10-10)*B3,0) =IF(B10>10,(10-B10)*B3,0) =(B10-10)*B3 =IF(B10>10,0,(B10-10)*B3) SUMPRODUCT(B10,B3) B10*B3
C) What formula should go into cell E10 to calculate the Refund amount?
B10*B4 =IF(B10>5,(B10-5)*B4,0) =IF(B10<5,0,B10*B4) =IF(B10<5,B10*B4,0) SUMPRODUCT(B10:B4) =IF(B10<5,(B10-5)*B4,0)
D) What formula should go into cell F10 to calculate the total money in the jar?
Full question attached:
Answer and explanation:
A) B2*B10: cell B2 and B10 have the values regular swear costs and number of swears respectively and we need to multiply these two values to get our answer
B) =IF(B10>10,(B10-10)*B3,0): Sam is supposed to pay an extra $2 for swear words over 10 and so we check if his swear words are above 10 and if they are we find out how many they are by subtracting 10 from them and then we multiply the value gotten by the cost for extra swear words($2)
C) =IF(B10<5,B10*B4,0): here we check if swear words are less than 5 and if they are we multiply number of swears words less than by 5 by the cost ($0.50)
D) F10=C10+D10+E10: to calculate total money in jar(F10), we simply add up regular cost(C10), extra cost(D10) and refund(E10)
Find a8 of the sequence 10,9.75,9.5,9.25,….
Answer:
10,9.75,9.5,9.25,9, 8.75 , 8.5, 8.25, 8...
Step-by-step explanation:
Subtract 0.25 from each to find the next number
Answer:
8.25
Step-by-step explanation:
If you substract .25 from each number until you get to a8 you will get 8.25
Find m A. 10 B. 5 C.√53 D. 10√3/3
Answer:
[tex]m = 10[/tex]
Step-by-step explanation:
Looking at the angles, we can see that this is a 30-60-90 triangle.
The side that is with the 30° angle and the 90° angle is represented by [tex]x\sqrt{3}[/tex].
So let's find x.
[tex]x\sqrt{3} = 5\sqrt{3}[/tex]
Divide both sides by [tex]\sqrt{3}[/tex]:
[tex]x = 5[/tex].
Now the hypotenuse is always [tex]2x[/tex] (the leg with the 90° and 60° is just x.) So,
[tex]2x = 2\cdot5 = 10[/tex].
Hope this helped!
What is the error in this problem?
Answer:
wrong position of tan 64
Help Me With This
show work
Answer:
1. Make a list of activities and the number of students:
Watching TV: 32
Talking on the phone: 41
Video games: 24
Reading: 15
2. Then combine the data in a bar graph as shown in the picture
A system of equations consists of the two equations shown.
{4x+5y=18
6x−5y=20
Which procedure will produce a single equation in one variable? Select all the procedures that apply.
A. Subtract the first equation from the second equation.
B. Subtract the second equation from the first equation.
C. Multiply the first equation by 18; multiply the second equation by 18; add the equations.
D. Multiply the first equation by − 6; multiply the second equation by 4; add the two equations.
E. Multiply the first equation by 3; multiply the second equation by − 2; add the two equations.
F. Multiply the first equation by 3; multiply the second equation by 2; subtract the equations in any order.
Answer:
C, D, E and F
Step-by-step explanation:
Given
4x+5y=18
6x−5y=20
Required
Determine which procedure will result in a single equation in one variable
To do this; we'll test each of the options
A. Subtract the first equation from the second equation.
[tex](6x - 5y=20) - (4x+5y=18)[/tex]
[tex]6x - 4x - 5y - 5y = 20 - 18[/tex]
[tex]2x - 10y = 2[/tex] --- This didn't produce the desired result
B. Subtract the second equation from the first equation.
[tex](4x+5y=18) - (6x - 5y=20)[/tex]
[tex]4x - 6x + 5y + 5y =18 - 20[/tex]
[tex]-2x + 10y = -2[/tex] --- This didn't produce the desired result
C. Multiply the first equation by 18; multiply the second equation by 18; add the equations.
First Equation
[tex]18 * (4x+5y=18)[/tex]
[tex]72x + 90y = 324[/tex]
Second Equation
[tex]18 * (6x - 5y=20)[/tex]
[tex]108x - 90y = 360[/tex]
Add Resulting Equations
[tex](72x + 90y = 324) + (108x - 90y = 360)[/tex]
[tex]72x + 108x + 90y - 90y = 324 + 360[/tex]
[tex]72x + 108x = 324 + 360[/tex]
[tex]180x = 684[/tex] --- This procedure is valid
D. Multiply the first equation by − 6; multiply the second equation by 4; add the two equations.
First Equation
[tex]-6 * (4x+5y=18)[/tex]
[tex]-24x - 30y = -108[/tex]
Second Equation
[tex]4 * (6x - 5y=20)[/tex]
[tex]24x - 20y = 80[/tex]
Add Resulting Equations
[tex](-24x - 30y = -108) + (24x - 20y = 80)[/tex]
[tex]-24x + 24x - 30y -20y = -108+ 80[/tex]
[tex]-50y = -28[/tex]
[tex]50y = 28[/tex] --- This procedure is valid
E. Multiply the first equation by 3; multiply the second equation by − 2; add the two equations.
First Equation
[tex]3 * (4x+5y=18)[/tex]
[tex]12x + 15y = 54[/tex]
Second Equation
[tex]-2 * (6x - 5y=20)[/tex]
[tex]-12x + 10y = -40[/tex]
Add Resulting Equations
[tex](12x + 15y = 54) + (-12x + 10y = -40)[/tex]
[tex]12x - 12x + 15y - 10y =54 - 40[/tex]
[tex]5y = 14[/tex] --- This procedure is valid
F. Multiply the first equation by 3; multiply the second equation by 2; subtract the equations in any order
First Equation
[tex]3 * (4x+5y=18)[/tex]
[tex]12x + 15y = 54[/tex]
Second Equation
[tex]2 * (6x - 5y=20)[/tex]
[tex]12x - 10y = 40[/tex]
Subtract equation 1 from 2 or 2 from 1 will eliminate x;
Hence, the procedure is also valid;
